### Primary Divisonal 2012/6

Posted:

**Thu Dec 11, 2014 1:21 pm**In this diagram, the area of the larger square is three times of the smaller one. The area of the black shaded part is $12$ square unit. Find the area of the bigger square.

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Posted: **Thu Dec 11, 2014 1:21 pm**

In this diagram, the area of the larger square is three times of the smaller one. The area of the black shaded part is $12$ square unit. Find the area of the bigger square.

Posted: **Thu Dec 11, 2014 2:27 pm**

Suppose,the area of the larger square is $x^{2}$ and the area of the smaller square is $y^{2}$.

So,$x^{2}=3y^{2}.

x=\sqrt{3}y$

$\frac{1}{2}\times (\sqrt{3}y+y)(\sqrt{3}y-y)=12$

Or,$\frac{1}{2}\times (3y^{2}-y^{2})=12$

Or,$y^{2}=12$

$\therefore x^{2}=36$

$\therefore$ The area of the bigger square is $36$ square unit

So,$x^{2}=3y^{2}.

x=\sqrt{3}y$

$\frac{1}{2}\times (\sqrt{3}y+y)(\sqrt{3}y-y)=12$

Or,$\frac{1}{2}\times (3y^{2}-y^{2})=12$

Or,$y^{2}=12$

$\therefore x^{2}=36$

$\therefore$ The area of the bigger square is $36$ square unit